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Update matrix_chain_order calculation with more details and test. (#12759)

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Mindaugas
2025-05-23 00:17:48 +03:00
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parent e1115b5f15
commit a8ad2db2b9
1 changed files with 23 additions and 10 deletions
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33
dynamic_programming/matrix_chain_order.py
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@ -5,13 +5,19 @@ Dynamic Programming
Implementation of Matrix Chain Multiplication Implementation of Matrix Chain Multiplication
Time Complexity: O(n^3) Time Complexity: O(n^3)
Space Complexity: O(n^2) Space Complexity: O(n^2)
Reference: https://en.wikipedia.org/wiki/Matrix_chain_multiplication
""" """
def matrix_chain_order(array): def matrix_chain_order(array: list[int]) -> tuple[list[list[int]], list[list[int]]]:
"""
>>> matrix_chain_order([10, 30, 5])
([[0, 0, 0], [0, 0, 1500], [0, 0, 0]], [[0, 0, 0], [0, 0, 1], [0, 0, 0]])
"""
n = len(array) n = len(array)
matrix = [[0 for x in range(n)] for x in range(n)] matrix = [[0 for _ in range(n)] for _ in range(n)]
sol = [[0 for x in range(n)] for x in range(n)] sol = [[0 for _ in range(n)] for _ in range(n)]
for chain_length in range(2, n): for chain_length in range(2, n):
for a in range(1, n - chain_length + 1): for a in range(1, n - chain_length + 1):
@ -28,26 +34,33 @@ def matrix_chain_order(array):
return matrix, sol return matrix, sol
# Print order of matrix with Ai as Matrix def print_optimal_solution(optimal_solution: list[list[int]], i: int, j: int):
def print_optiomal_solution(optimal_solution, i, j): """
Print order of matrix with Ai as Matrix.
"""
if i == j: if i == j:
print("A" + str(i), end=" ") print("A" + str(i), end=" ")
else: else:
print("(", end=" ") print("(", end=" ")
print_optiomal_solution(optimal_solution, i, optimal_solution[i][j]) print_optimal_solution(optimal_solution, i, optimal_solution[i][j])
print_optiomal_solution(optimal_solution, optimal_solution[i][j] + 1, j) print_optimal_solution(optimal_solution, optimal_solution[i][j] + 1, j)
print(")", end=" ") print(")", end=" ")
def main(): def main():
"""
Size of matrix created from array [30, 35, 15, 5, 10, 20, 25] will be:
30*35 35*15 15*5 5*10 10*20 20*25
"""
array = [30, 35, 15, 5, 10, 20, 25] array = [30, 35, 15, 5, 10, 20, 25]
n = len(array) n = len(array)
# Size of matrix created from above array will be
# 30*35 35*15 15*5 5*10 10*20 20*25
matrix, optimal_solution = matrix_chain_order(array) matrix, optimal_solution = matrix_chain_order(array)
print("No. of Operation required: " + str(matrix[1][n - 1])) print("No. of Operation required: " + str(matrix[1][n - 1]))
print_optiomal_solution(optimal_solution, 1, n - 1) print_optimal_solution(optimal_solution, 1, n - 1)
if __name__ == "__main__": if __name__ == "__main__":